Solve 1/3/x=1-1/x/x

$$\frac { \frac { 1 } { 3 } } { x } = \frac { 1 - \frac { 1 } { x } } { x }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{1}{3}=1-\frac{1}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{1}{3}=\frac{x}{x}-\frac{1}{x}$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}=\frac{x-1}{x}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x-1}{x}=\frac{1}{3}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of x,3.

$$3\left(x-1\right)=x$$

Use the distributive property to multiply 3 by x-1.

$$3x-3=x$$

Subtract x from both sides.

$$3x-3-x=0$$

Combine 3x and -x to get 2x.

$$2x-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$2x=3$$

Divide both sides by 2.

$$x=\frac{3}{2}$$